The Chaocipher
Challenge: Progress Report #2

In the previous episode ...

In
progress report #1
I theorized about a cipher system that would simulate the fact that
pt/ct identities do not occur at distances less than 9, then
promptly rejected the system as the basis for Chaocipher.
Since then I have come up with a system that is closer to
observable traits in Chaocipher. In this progress report
I describe this newer hypothetical system.

A
newer hypothetical system

We can state the pt/ct identities issue as follows:

A pt/ct identity will not occur within a distance of N if a key does not occur again for the next N letters.

I'm
now looking at a contrived
hypothetical system which would explain the distance < 9 AND the
second ct letters of doubled plaintext letters. It does this by
guaranteeing that a key is not encountered for 8 more letters after
being used. This system is decidedly not the Chaocipher. The
point is to concoct a system that will prevent pt/ct identities in
distances less than 9 and will allow more latitude than the system in
report #1. This will give us a model somewhat closer to the
Chaocipher, allowing us to hopefully hypothesize in the right direction.

The system
assumes:

Two alphabetic slides, pt and ct.
The ordering of the alphabets is not relevant for this discussion.

A list
of the possible key designations (e.g., 1-26, 0-25, or A-Z) in any
order.

We have a reproduceable method for
generating a number greater than 8.

The system
works like this:

Use the key designator at
the head of the list as the key.

Encipher the
plaintext letter using the alphabetic slides and the key letter.

Generate
a number 9 <= N <= 26

Remove the head of the key
designator list, leaving 25 letters in the list.

Insert
the just-discarded key designator as the Nth element of the list

Repeat
from step (1)

Let's see an example

Alphabet
slides

For
simplicity we'll use the straight alphabet for both pt and ct slides:

Enciphering
will be done by locating the key letter on the ct slide, positioning
this letter under the pt slide's 'A'. For example, to
encipher the plaintext letter 'F' using a key letter of 'R', position
the slides as follows:

Discussion

The above system is an improvement on the +1 / +2 / +3 model in progress report #1 because:

The
new system prevents pt/ct identities within distances less than 9.
It does this by "throwing" a key used for enciphering at least 9
positions into the future.

When plaintext doubles (e.g., "XX"
in the above example) are enciphered, the second ciphertext letter can
be any letter other than the first ciphertext letter). This was a
problem with the old system in progress report #1, but is no longer a
problem here.

A mistake made while enciphering will garble the remaining message.

The new system has its drawbacks:

Letters
at the end of the key designator list tend to stay at the end for quite
some time. For example, the last letter in the key designator
list will remain at the end until a key letter is positioned in slot 26.

An
enciphering mistake will not necessarily immediately garble everything
from this point onwards. It could take quite a few encipherings
until an incorrectly decimated key letter makes itself felt. This
may be counter to the comment in Deavours and Kruh: "And, an important shortcoming of the cipher -- make one error during encipherment and the message is garbled beyond repair ..." [1].

Nonetheless, I believe this system is a step forward in the right direction.

References

[1]
John Byrne, Cipher A. Deavours and Louis Kruh. Chaocipher
enters
the computer age when its method is disclosed to Cryptologia
editors. Cryptologia, 14(3): 193-197.